The Kansas City Federal Reserve has the evidence. It says the number of free checking accounts in the U.S. grew from 19.4% in 2011 (the year the Durbin rule was enacted) to 21.6% last year. "For an average consumer, free checking became more available after interchange fee regulation," the Kansas City Fed says in the study.

Customers at smaller banks, which were exempt from the Durbin Amendment, didn't see charges on checking accounts, while financial institutions with more than $10 billion in assets sought ways to compensate for revenues lost from limits on debit card fees.

"Thus, consumers' net increase in access to free checking stemmed mainly from the greater availability of free checking at exempt banks," the Federal Reserve report says. "Elimination of free checking accounts at larger, regulated banks was more than offset by an increase in free checking accounts at smaller, exempt banks."

Stiffer competition among banks has also helped keep checking account fees down, according to the Kansas City Fed.

"This [study] finds evidence that access to free checking has expanded most in cities and regions where banks are engaged in vigorous competition: banks in such markets may offer free checking to attract customers from other banks or to ensure retention of their own established customers," the report adds.